In a large, shallow dish, combine the ouzo, lemon juice and cayenne. Add the shrimp and toss to coat thoroughly. Cover and refrigerate for at least 1 1/2 hours or for up to 2 hours.
Dry the shrimp. In a large skillet, heat 1 1/2 tablespoons of the oil until shimmering. Add half of the shrimp and cook over high heat, stirring, until golden and just cooked, 2 minutes. Season with salt and transfer to a platter. Repeat with the remaining oil and shrimp. Serve hot or warm.
A light-bodied, southern Mediterranean white with a hint of lemon will echo the lightness of the shrimp.